He reportedly told one Republican senator in January: "We don't think that was my voice."
And his private questioning of the tape has continued right up until recent days.
The comments contradict Mr Trump's unequivocal response to the video in the final days of the 2016 election campaign where he said the voice on the tape was his.
"I said it, I was wrong and I apologise," Mr Trump said.
Access Hollywood, for its part, has slammed suggestions the tape was faked.
"Let us make this perfectly clear — the tape is very real," host Natalie Morales said on Monday.
"Remember his excuse at the time was 'locker-room talk'. He said every one of those words."
The new doubts come as allegations of sexual harassment — including a barrage directed at Mr Trump himself — engulf Washington and Hollywood.
But Mr Trump's private talk of conspiracy theories doesn't stop there.
The Times reports that he continues to question whether Mr Obama was really born in the US, despite the White House releasing the former president's birth certificate in 2011, which proved he was born in Hawaii in 1961.
Mr Trump was the leading public voice of the bogus "birther" movement, until he finally acknowledged (through gritted teeth) in a speech in 2016 that "President Barack Obama was born in the United States — period".
The President also believes that he lost the popular vote in the election due to pervasive voter fraud, despite the fact that numerous studies say the practice is so rare as to be "virtually non-existent".
On his first day in office, Mr Trump implied the news media had conspired to understate the size of the crowd in attendance at his inauguration.
He sent his press secretary Sean Spicer into the White House press briefing room to say "this was the largest audience to ever witness an inauguration, period, both in person and around the globe". Even Mr Spicer now admits that claim was incorrect.
And while Mr Trump appears to have moved on from that conspiracy, he spouted a new one as recently as Wednesday on Twitter.
In an extraordinary tweet, Mr Trump implied that one of his strongest critics, cable news host Joe Scarborough, may have had something to do with the death of an employee.
The "unsolved mystery" Mr Trump refers to is the death of Lori Klausutis, 28, an intern who was found dead in Scarborough's Florida office in 2001 when he was still a Republican congressman.
To be clear, there is no mystery in her death. The medical examiner concluded that Ms Klausutis "lost consciousness because of an abnormal heart rhythm and fell, hitting her head on a desk".
"The head injury caused the death," he said a month after she was found dead.
There is no evidence of foul play and Scarborough dismissed the allegation by saying Mr Trump "is not well".
Mr Trump was also caught out overnight retweeting a fake video from a far-right UK political leader.
The video, which he shared with his 43 million followers, had the caption "Muslim migrant beats up Dutch boy on crutches", but it turns out the perpetrator was not a Muslim migrant, but a native Dutchman.
When asked about it, White House spokeswoman Sarah Huckabee Sanders said it didn't matter whether the video was real or not.
"Whether it's a real video, the threat is real, and that is what the President is talking about," she told reporters.
In an opinion piece, The Washington Post went so far as to argue that Mr Trump's lies "strengthen the case for his removal".
"He operates with facts of his own in a world of his own. He makes fools of his friends, enemies of critics and truth out of lies. He may not be danger to himself, but he is to the rest of us. On a daily basis, he makes an increasingly strong case for removal," columnist Richard Cohen wrote.
